Talks and Poster Presentations (without Proceedings-Entry):
W. Auzinger:
"Exponential and rational multistep methods";
Talk: Second joint Conference of Austrian and Mongolian Mathematicians,
Ulaanbaatar (invited);
2011-10-21
- 2011-10-22.
English abstract:
Rational multistep methods are a blend of one-step and multistep methods, for the purpose of efficient integration of stiff systems of differential equations, especially after semi-discretization of evolutionary partial differential equations. For a semi-linear stiff system u'(t) = Au(t)+ f(t,u(t)), u(0) = u0, a rational multistep integrator involves an A-stable rational approximation of the (stiff) linear part in combination with a multistep ansatz for the (non-stiff or mildly stiff) nonlinear part.
Since the 1970īs, several authors have proposed such schemes, but a convergence analysis has not been available until recently. It has been demonstrated how rational multistep schemes can be interpreted in a natural way as rational modifications of so-called exponential multistep schemes. This point of view reveals a strategy to analyze convergence and to obtain rigorous error bounds. We explain this approach, discuss its interrelation with exponential schemes, and sketch the convergence proof for the so-called Adams-Padé version, making use of results from approximation theory concerning the error of Padeé approximations to the matrix exponential exp(tA). Furthermore, implementation issues and numerical examples are discussed.
Created from the Publication Database of the Vienna University of Technology.